Question

Log3(x-4)=2 как решить?

Answer 1

Log₃(x-4)=2
x-4>0
x>4
log₃(x-4)=log₃9
x-4=9
x=9+4
x=13 (>4)
Ответ: 13

Answer 2

Solving the Equation Log3(x-4)=2

To solve the equation Log3(x-4)=2, we can use the properties of logarithms to isolate the variable x. Let's go through the steps to solve this equation.

1. Isolate the Logarithm: We can start by isolating the logarithm term on one side of the equation.

2. Apply the Inverse Operation: Once the logarithm is isolated, we can apply the inverse operation to both sides of the equation to solve for x.

3. Check the Solution: After finding the value of x, it's important to check the solution by substituting it back into the original equation to ensure it satisfies the equation.

Now, let's proceed with the solution using the given equation.

Solution Steps:

1. Isolate the Logarithm: We have the equation Log3(x-4)=2. To isolate the logarithm, we can rewrite it in exponential form. The base of the logarithm is 3, and the result is 2, so we can express it as: 3^2 = x - 4.

2. Solve for x: By solving the exponential equation, we can find the value of x. 3^2 = x - 4 9 = x - 4 x = 9 + 4 x = 13

3. Check the Solution: Substituting x = 13 back into the original equation: Log3(13-4) = 2 Log3(9) = 2 2 = 2

The solution x = 13 satisfies the original equation.

Therefore, the solution to the equation Log3(x-4)=2 is x = 13.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.